"Accumulated estimates from the three countries put the total number of affected people between 1.5 million and 1.8 million," Elisabeth Byrs, UN humanitarian afairs agency spokeswoman, said.
Helicopters were urgently needed to reach isolated villages under water in Somalia, where relief operations are hampered by conflict, she said.
Epidemics linked to polluted, stagnant water - including cholera, malaria and dysentery - are feared, so products to treat water and mosquito nets are urgently needed, Byrs said.
Kenya's health ministry has reported 13 cases of cholera and two deaths.
The UNHCR refugee agency will fly emergency fuel, medicines and plastic sheets to Dadaab on Sunday, where some 160,000 mostly Somali refugees are sheltering in low-lying settlements after fleeing growing tensions in their homeland.
"People were actually telling us that the present flooding is worse than the El Nino floods in 1997 that submerged most of eastern Kenya."
spokesman for the World Food Programme
"If roads in the region remain impassable, UNHCR expects to mount further flights next week," it said in a statement.
At least 47 people have died in floods in southern Somalia described as the worst for 50 years, and one charity said up to half a million children there needed emergency aid.
Kenya has reported more than 25 killed, according to the UN's World Food Programme (WFP).
The UNHCR said the hospital at one refugee camp in Kenya had been badly damaged by the floods, and that its staff were digging dikes and stacking sandbags to try to protect other medical centres.
Kenyans living around the camps had also been affected, it added, and had turned to the UN for help.
Tens of thousands of people have fled their homes in the region in recent weeks, especially in Somalia, where many sleep outdoors in unsanitary conditions, according to the UN children's fund.
WFP said it had distributed emergency food rations to the Ifo camp in Kenya, which holds 54,000 refugees.
It planned to airlift 190 metric tonnes of high-energy biscuits for 100,000 mainly Somali refugees and 100,000 Kenyans living in the Dadaab region of eastern Kenya.
"People were actually telling us that the present flooding is worse than the El Nino floods in 1997 that submerged most of eastern Kenya," Simon Pluess, WFP spokesman, said.